scholarly journals User online consumption behaviour based on fractional differential equation

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Dongya Zhou ◽  
Lixia Li ◽  
Bahjat Fakieh ◽  
Ragab Ibrahim Ismail
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Consumer Behaviour ◽  
Equation Model ◽  
Differential Equation Model ◽  
Consumption Behaviour ◽  
Two Factors ◽  
Fractional Differential ◽  
The Cost ◽  
The Impact

Abstract User consumption behaviour is a subject worthy of study. Because consumers’ consumption behaviours are dynamic and with individual differences, various factors need to be considered when establishing a fractional differential equation model of users’ online consumption behaviour. The two elements, namely advertising and price are more evident in influencing consumer behaviour. Therefore, the paper establishes a product diffusion fractional differential equation model of price and advertising presence or absence to study the impact of these two factors on consumer behaviour. It turns out that ignoring the advertisement and the cost of the product is related to the characteristics of the consumer network. When there are advertising and price factors, product awareness is related to price constraints.

Time Fractional Differential Equation Model With Random Derivative Order

2009 ◽  
Author(s):  
Hongguang Sun ◽  
Yangquan Chen ◽  
Wen Chen
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Diffusion Processes ◽  
Time Derivative ◽  
Equation Model ◽  
Differential Equation Model ◽  
New Model ◽  
Potential Applications ◽  
Fractional Differential ◽  
Derivative Order

This paper proposes a new type of fractional differential equation model, named time fractional differential equation model, in which noise term is included in the time derivative order. The new model is applied to anomalous relaxation and diffusion processes suffering noisy field. The analysis and numerical simulation results show that our model can well describes the feature of these processes. We also find that the scale parameter and the frequency of the noise play a crucial role in the behaviors of these systems. At the end, we recognize some potential applications of this new model.

scholarly journals Effects of masks on the transmission of infectious diseases

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Lili Han ◽  
Qiuhui Pan ◽  
Baolin Kang ◽  
Mingfeng He
Keyword(s):  
Differential Equation ◽  
Numerical Simulation ◽  
Infectious Diseases ◽  
Reproduction Number ◽  
Quantitative Description ◽  
Equation Model ◽  
Differential Equation Model ◽  
High Incidence ◽  
The Impact ◽  
The Basic Reproduction Number

AbstractIn the present paper, based on the conditions that asymptomatic virus carriers are contagious and all symptomatic infected individuals wear masks, we study the impact of wearing masks in the susceptible and the asymptomatic virus carriers on the spread of infectious diseases by developing a differential equation model. At first, we give the existence, uniqueness, boundedness, and positivity of the solution as well as the basic reproduction number $R_{0}$ R 0 for the established model. Then, for two cases of wearing masks in the susceptible and the asymptomatic virus carriers where the proportion of wearing masks is fixed and the proportion of wearing masks changes with time, the results of the numerical simulation are shown in a series of pictures, and quantitative description of effects of the proportion of the population wearing masks, the protective effect of masks, and the time when they start wearing masks on the epidemic is given. Our results show that under the situation that the proportion of wearing masks is positively related to the confirmed new cases and new deaths, though the proportion will be close to 1 during the high incidence of patients, the effect on controlling the spread of such infectious diseases is far worse than the case of always maintaining a relatively higher proportion (≥0.66) of wearing masks.

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